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Hoxha, Ilmi,Braha, Naim Latif Korean Mathematical Society 2014 대한수학회지 Vol.51 No.5
An operator $T{\in}L(H)$, is said to belong to k-quasi class $A_n^*$ operator if $$T^{*k}({\mid}T^{n+1}{\mid}^{\frac{2}{n+1}}-{\mid}T^*{\mid}^2)T^k{\geq}O$$ for some positive integer n and some positive integer k. First, we will see some properties of this class of operators and prove Weyl's theorem for algebraically k-quasi class $A_n^*$. Second, we consider the tensor product for k-quasi class $A_n^*$, giving a necessary and sufficient condition for $T{\otimes}S$ to be a k-quasi class $A_n^*$, when T and S are both non-zero operators. Then, the existence of a nontrivial hyperinvariant subspace of k-quasi class $A_n^*$ operator will be shown, and it will also be shown that if X is a Hilbert-Schmidt operator, A and $(B^*)^{-1}$ are k-quasi class $A_n^*$ operators such that AX = XB, then $A^*X=XB^*$. Finally, we will prove the spectrum continuity of this class of operators.
Ilmi Hoxha,Naim Latif Braha 대한수학회 2014 대한수학회지 Vol.51 No.5
An operator T ∈ L(H), is said to belong to k-quasi class A∗n operator if T∗k(|Tn+1|2/n+1 - |T∗|2)Tk≥O for some positive integer n and some positive integer k. First, we will see some properties of this class of operators and prove Weyl’s theorem for algebraically k-quasi class A ∗ n . Second, we consider the tensor product for k-quasi class A ∗ n , giving a necessary and sufficient condition for T ⊗ S to be a k-quasi class A ∗ n , when T and S are both non-zero operators. Then, the existence of a nontrivial hyperinvariant subspace of k-quasi class A ∗ n operator will be shown, and it will also be shown that if X is a Hilbert-Schmidt operator, A and (B ∗ ) −1 are k-quasi class A ∗ n operators such that AX = XB, then A ∗ X = XB ∗ . Finally, we will prove the spectrum continuity of this class of operators.
Spase Shumka,Yukio Nagahama,Sarjmir Hoxha,Koji Asano 한국수산과학회 2023 Fisheries and Aquatic Sciences Vol.26 No.4
Beside that the fish species and their sub-populations are highly important as a keystone species in the coastal and marine ecosystem, there are very few studies on their presence, distribution and temporal variations within and around the lagoon ecosystems in Albania. This paper provides an updated review on the life cycle, fishery, exploitation state and management of the main species that are subject of commercial fishing in the Karavasta lagoon, southeastern Adriatic coast of Albania. Due to the fact that lagoons represent a continuum between continental and marine aquatic ecosystems they play a crucial role in species life cycles. Further on in the circumstances of rapid utilizations and environmental changes, anomalies in salinity and temperatures, accelerated anthropogenic influences their rate of vulnerability is highly increased. Following the requirements of the Water Framework Directive, transitional water, coastal lagoons and estuaries there is a need for urgent monitoring and management approaches. The commercial species include: European eel (Anguilla anguilla), species of Family Mugilidae (Mugil cephalus, Liza ramada, Liza salienes and Chelon labrosus), Seabream (Sparus aurata), Seabass (Dincentrarchus labrax), etc. Fish productivity is oscillating from maximum value of 61.95 kg/ha is recorded in period of 1975–80 and lower value of 31 kg/ha in year 2020. Our study highlights importance of fish and fishery long-term monitoring, and contributes to understand the driving factors in productivity, migration patterns and species ecology in the vital coastal ecosystems.
Bubble-free rapid microfluidic PCR
Lee, Sang Hun,Song, Jihwan,Cho, Byungrae,Hong, SoonGweon,Hoxha, Ori,Kang, Taewook,Kim, Dongchoul,Lee, Luke P. Elsevier 2019 Biosensors & Bioelectronics Vol.126 No.-
<P><B>Abstract</B></P> <P>Microfluidic polymerase chain reaction (PCR) has been of great interest owing to its ability to perform rapid and specific nucleic acid amplification and analysis on small volumes of samples. One of the major drawbacks of microfluidic PCR is bubble generation and reagent evaporation, which can cause malfunctions. Here, through theoretical modeling and characterization of bubble behavior, we propose a bubble-free microfluidic PCR device via controlled fluid transfer. Our approach exploits a thin impermeable polyethylene (PE) top layer that minimizes the generation of bubbles by inhibiting mass transport along a vertical direction. Simulation results demonstrate that a calculated mass flow difference of approximately 370% can be obtained by utilizing an impermeable membrane as the vertical barrier layer. To demonstrate proof-of-concept, two nanoporous polymeric materials, poly(dimethylsiloxane) (PDMS) and PE, were used for stand-alone self-powered sample loading (approximately 70 s) and for use as a vertical barrier layer, respectively. Consequently, we demonstrate successful amplification of the cMET gene, a nucleic acid (NA) biomarker for lung cancer, and complete an ultrafast PCR test in less than 3 min using a high powered Peltier-based thermal cycler under bubble-free conditions. This approach will result in a new paradigm for ultrafast molecular diagnosis and can facilitate NA-based nearly instantaneous diagnostics for point-of-care testing and for personalized and preventive medicine.</P> <P><B>Highlights</B></P> <P> <UL> <LI> The major drawbacks of microfluidic PCR is bubble generation and reagent evaporation. </LI> <LI> A bubble-free microfluidic PCR device via controlled fluid transfer through theoretical modeling and characterization of bubble behavior. </LI> <LI> An impermeable polyethylene layer minimizes the generation of bubbles by inhibiting mass transport along a vertical direction. </LI> <LI> The microfluidic PCR chamber design with surrounding circumferential chamber for a guided-fluid transport of generated bubble. </LI> <LI> Successful nucleic acid amplification of the cMET gene, and an ultrafast PCR test in less than 3 min. </LI> </UL> </P> <P><B>Graphical abstract</B></P> <P>[DISPLAY OMISSION]</P>